CN109446611B - Shape finding optimization design method for strong coupling tree-shaped structure - Google Patents
Shape finding optimization design method for strong coupling tree-shaped structure Download PDFInfo
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Abstract
The invention provides a shape finding optimization design method of a strong coupling tree-shaped structure, which comprises the following steps: setting initial parameters; establishing a tree structure with a double-unit numerical model; if m is an odd number, applying a reverse load; solving the internal force of each branch, and calculating the temperature load of all branches; if m is an even number, applying a temperature load; extracting vertical displacement of all nodes; changing the position of the node according to the vertical displacement of the extraction point; and ending the shape finding process until the maximum node displacement is smaller than the threshold value. The invention adopts a double-unit numerical model, the cross-sectional area of the rod unit is far larger than that of the beam unit, and a very small bending rigidity is given to the beam unit, so that the problem that the double-unit tree model cannot be solved due to the fact that the rigidity matrix is not of a full rank is solved; the invention has high precision and high efficiency, avoids heavy programming work, couples two works of optimization and shape finding into an iterative program, has high convergence speed and ensures the maximization of the integral stable bearing capacity of the tree structure.
Description
Technical Field
The invention relates to the technical field of building structure engineering, in particular to a shape finding optimization design method for a strong coupling tree-shaped structure.
Background
Tree structures are increasingly being used because of their attractive appearance and their efficient form of load transfer. The tree structure can efficiently transmit vertical load in a large range to one point on the ground, so that the tree structure is widely applied to large building structures. Due to the aesthetic appearance, tree structures tend to be landmark buildings. Many researchers have studied it because of its good mechanical properties.
Through the reasonable arrangement and arrangement of the spatial positions of all the branches of the tree structure, all the branches of the tree structure can be only under the action of axial pressure. Therefore, the main problem of tree-like structure is to find the most reasonable stress form by shape-finding analysis. At present, a calculation method related to the shape finding of the tree-shaped structure is mainly provided by Kolodziejczyk, which is to immerse a silk thread model in water and realize the shape finding of the tree-shaped structure by utilizing the surface tension of the water; buelow proposes a dry filament model method to find the shape of the tree-like structure; hunt proposes that all nodes of a tree structure are regarded as hinged, then a vertically sliding virtual support is applied, and shape finding is carried out by iteratively reducing the counter force of the virtual support; the shape-finding of the tree structure is carried out through continuous cable units proposed by Chenshihua and the shape-finding method is proposed by Wuyue, all branches of the tree structure generated by the shape-finding method are only under the action of axial force, and the requirement of shape finding is completely met.
At present, a plurality of methods related to shape finding of a tree structure are available and mature. But most of them need heavy programming process and are difficult to be mastered by vast engineers. Therefore, actively exploring a simpler and more practical shape finding method is beneficial to the popularization and application of the tree structure. In addition, the existing shape finding method does not optimize the geometric length of each branch. As is known, after the tree structure is found, each branch of the tree structure is only under the action of axial pressure, and the branch can be unstable under the action of the pressure. The minimum stable load capacity of all branches determines the stable load capacity of the entire tree. Therefore, optimizing the stable load bearing capacity of the rod can improve the stable load bearing capacity of the overall structure, and little research has been done at present.
Disclosure of Invention
In order to solve the problem that the programming process which needs to be heavy is still difficult to master by vast engineering technicians, the invention provides a numerical analysis method for carrying out shape finding analysis on a tree structure by utilizing an iterative process of a double-unit numerical model, on the basis, the geometric length of each branch is optimized by utilizing the internal force of each branch under the action of a given load, and an efficient iterative algorithm-tree structure strong coupling shape finding optimization algorithm integrating shape finding and optimization is provided. A shape finding optimization design method of a strong coupling tree-shaped structure comprises the following processes:
step 1: setting initial parameters according to design requirements, comprising: setting the position of applying load according to design or actual requirements, wherein the node coordinate of applying load is fixed in the iteration process; setting the calculated length coefficient mu of each cell according to the node stiffness, mu in the following formula i Means the calculated length coefficient for the ith branch;
and 2, step: establishing a double-unit numerical model, forming a tree structure with the double-unit numerical model according to initial parameters, wherein a trunk is in the vertical direction, each branch of the tree structure is a double-unit numerical model, the double-unit numerical model comprises a beam unit and a rod unit, the section area a of the beam unit and the section area A of the rod unit are set, and the axial inertia moment I of the beam unit is set;
the method for establishing the double-unit model comprises the following steps: a common beam element numerical model is established in finite element software, a beam element is copied, the copied beam element type is changed into a rod element model, the node number is unchanged, and the beam element and the rod element are called a double-element numerical model together.
The cross-sectional area of the rod unit in each double-unit numerical model is 100-10000 times of that of the beam unit.
And step 3: setting an initial value of a positive integer m to be 1;
and 4, step 4: if m is an odd number, applying a reverse load, namely a vertically upward point load, to the tree structure with the double-unit numerical model;
and 5: carrying out nonlinear static analysis on the tree structure with the double-unit numerical model applying the reverse load, and solving the internal force of each branch, wherein the axial internal force of the ith branch is F i (ii) a Extracting all node horizontal displacement, wherein the horizontal displacement of the j-th node is d xj And d yj (ii) a Extracting the geometric length of all branches, wherein the geometric length of the ith branch is l i Calculating the temperature load delta T of all branches according to the axial force of each branch according to the following steps, wherein the steps comprise step 5.1-step 5.5:
step 5.1: obtaining the stable limit bearing capacity F of each branch after optimization according to the compression bar stability and Euler bearing capacity formula cri ：
Wherein, E i Means the modulus of elasticity, I, of the material used for the ith branch i Axial moment of inertia, l, of the beam unit of the ith branch i Geometric length of the ith branch,. mu. i Means the calculated length coefficient for the ith branch;
and step 5.2: calculating the ratio R of the actual internal force to the stable bearing force of the branch under the given load:
wherein R is i Is the ratio of the actual internal force to the steady bearing force of the ith branch under a given load, F i Is the axial internal force of the ith branch;
step 5.3: calculating the average value R of the ratio of the actual internal force to the stable bearing force of the branch under the given load ave ：
Wherein n is the number of all branches;
step 5.4: calculation of R i And R ave Difference Δ R of i When Δ R i When it is negative, i.e. R ave Less than R i Then the internal force of the branch is large, then a negative temperature load is applied to reduce the branch geometry length, otherwise a positive temperature load is applied to increase the branch geometry length:
△R i ＝R ave -R i (4)
step 5.5: calculating the temperature load DeltaT of the branch:
wherein A is i Is the cross-sectional area of the ith branch unit, alpha i The linear expansion coefficient of the ith branch;
step 6: changing the node position according to the extracted node horizontal displacement, wherein the jth node position is changed to: x is the number of j ＝x j +d xj ,y j ＝y j +d yj ，x j For the horizontal x-axis position, y, of the j-th node j Horizontal y-axis position for j-th node;
and 7: if m is an even number, applying a temperature load to the tree structure with the double-unit numerical model according to the temperature load numerical value calculated in the step 5;
and 8: in finite element software, the vertical and horizontal freedom degrees of the top node of the tree structure are restrained by applying a displacement restraining mode, and all the freedom degrees of the bottom node of the trunk are restrained simultaneously.
And step 9: and performing nonlinear static analysis, and extracting vertical displacement of all nodes, wherein the vertical displacement of the jth node is as follows: d zj ；
Step 10: changing the node position according to the extraction point vertical displacement, wherein the jth node position is changed to: z is a radical of j ＝z j +d zj ，z j Is the vertical z-axis position of the jth node;
step 11: judging whether the maximum node displacement isLess than threshold, i.e. Max (d) xj ,d yj ,d zj )<And (4) error, wherein the error is a threshold, if yes, the shape finding process is ended, otherwise, m is m +1, and the step returns to the step 4 to carry out shape finding again.
The beneficial technical effects are as follows:
1. since each line cell of the two-cell numerical model is composed of two cells, i.e., a rod cell and a beam cell. The cross-sectional area of the rod unit is far larger than that of the beam unit, and the beam unit is endowed with small bending rigidity, so that the problem that the dual-unit tree model cannot be solved due to the fact that the rigidity matrix is not of a full rank is solved.
2. The shape finding iterative program based on the double units has high precision and high efficiency, and avoids heavy programming work.
3. The length of each branch is optimized according to the Euler stable bearing capacity of the compression bar, so that the maximization of the integral stable bearing capacity of the tree-shaped structure can be ensured.
4. And (4) adjusting the length of each branch through repeated iteration by a form finding optimization iterative program, so that the internal force ratio of each branch tends to be the same.
5. The method can couple the two works of optimization and shape finding in an iterative program, and has high convergence speed.
Drawings
FIG. 1 is a schematic diagram of a dual cell implementation of the present invention;
FIG. 2 is a flow chart of a shape-finding optimization design method for a strongly coupled tree structure according to an embodiment of the present invention;
FIG. 3 is a schematic representation of the initial shape and loading of the tree structure of example 1 in an embodiment of the present invention;
FIG. 4 is a schematic diagram of the internal force of the tree structure after shape finding in example 1;
wherein, (a) is the schematic view of the bending moment of the tree-shaped structure after the shape finding of the calculation example 1; (b) is a schematic diagram of the axial force of the tree-shaped structure after shape finding of the calculation example 1;
FIG. 5 is a schematic diagram showing a comparison of the tree structure after shape finding in example 1 in the embodiment of the present invention;
wherein (a) is the result obtained by the present invention; (b) results obtained for Hunt;
FIG. 6 is a schematic diagram of tree hierarchy and geometric length in accordance with an embodiment of the present invention;
FIG. 7 is a schematic diagram of the initial shape of a tree structure in an embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating the change of the morphology of the tree structure during the optimization process according to the embodiment of the present invention;
wherein (a) is the 10 th time; (b) 50 th time; (c) is the 100 th time; (d) is the 200 th time; (e) 300 th time; (f) 500 th time; (g) 1000 th time; (h) 2000 th time; (i) 6000 times; (j) 10000 times;
FIG. 9 is a cloud of internal forces of a tree structure optimized in accordance with an embodiment of the present invention;
wherein, (a) is a bending moment cloud chart with a tree structure; (b) is a tree-structured axial force cloud picture;
FIG. 10 is a graph of convergence in an embodiment of the present invention;
FIG. 11 is a schematic diagram illustrating tree structure optimization results under different calculated length coefficients in an embodiment of the present invention;
wherein (a) s I And mu I ；(b)s I And mu II ；(c)s I And mu III ；(d)s I And mu IV
FIG. 12 is a schematic diagram of a spatial tree structure in an embodiment of the present invention;
wherein, (a) is a spatial tree structure front view; (b) is a spatial tree structure top view;
FIG. 13 is a cloud of internal forces in a spatial tree structure in accordance with an embodiment of the present invention;
wherein, (a) is a space tree-shaped structure axial force cloud picture; (b) a space tree-shaped structure bending moment cloud picture;
FIG. 14 is a diagram illustrating tree structure optimization results for different calculated length coefficients in an embodiment of the present invention;
wherein (a) is s I And mu I Top, front, perspective views of; (b) is s is I And mu II Top view, front view, perspective view.
Detailed Description
The invention will be further described with reference to the accompanying drawings and specific examples: a shape-finding optimization design method for a strongly coupled tree-shaped structure is shown in FIG. 2, and comprises the following processes:
step 1: setting initial parameters according to design requirements, comprising: the height, the section size and the total grading number of the tree structure are divided into 4 grades, the load applying position is set according to design or actual needs, and the node coordinate of the load applying position is fixed in the iteration process; setting the calculated length coefficient mu of each cell according to the node stiffness, mu in the following formula i Means the calculated length coefficient for the ith branch;
step 2: establishing a double-unit numerical model, forming a tree structure with the double-unit numerical model according to initial parameters, wherein a trunk is in the vertical direction, each branch of the tree structure is a double-unit numerical model, each double-unit numerical model comprises a beam unit and a rod unit, as shown in fig. 1, the cross section area a of the beam unit and the cross section area A of the rod unit are set, and the axial inertia moment I of the beam unit is set; the tree structure shown in fig. 3 is subjected to shape finding analysis based on the above proposed iterative procedure. In the two-unit numerical model for tree structure, the cross-sectional area of the rod unit is set to 1 × 10 -3 m 2 The cross-sectional area of the beam unit is set to 1X 10 -6 m 2 Axial moment of inertia of the beam unit being 2 x 10 -10 m 4 。
The method for establishing the double-unit model comprises the following steps: a common beam element numerical model is established in finite element software, a beam element is copied, the copied beam element type is changed into a rod element model, the node number is unchanged, and the beam element and the rod element are called a double-element numerical model together.
The cross-sectional area of the rod unit in each double-unit numerical model is 100-10000 times of that of the beam unit. The cross-sectional area of the rod unit is far larger than that of the beam unit, and the beam unit is endowed with small bending rigidity, so that the problem that the dual-unit tree model cannot be solved due to the fact that the rigidity matrix is not of a full rank is solved. Due to the fact that the double-unit numerical model has small bending rigidity, the tree-shaped structure can be well simulated through the double-unit numerical model.
And step 3: setting the initial value of a positive integer m to be 1;
and 4, step 4: if m is an odd number, applying a reverse load, namely a vertical upward point load, to the tree structure with the double-unit numerical model by 10 kN;
and 5: carrying out nonlinear static analysis on the tree structure with the double-unit numerical model applying the reverse load to solve the internal force of each branch, wherein the axial internal force of the ith branch is F i (ii) a Extracting all node horizontal displacement, wherein the horizontal displacement of the j-th node is d xj And d yj (ii) a Extracting the geometric length of all branches, wherein the geometric length of the ith branch is l i Calculating the temperature load delta T of all branches according to the axial force of each branch according to the following steps, wherein the steps comprise step 5.1-step 5.5:
step 5.1: obtaining the stable limit bearing capacity F of each branch after optimization according to the compression bar stability and Euler bearing capacity formula cri ：
Wherein E is i Means the modulus of elasticity, I, of the material used for the ith branch i Is the axial moment of inertia, mu, of the beam element of the ith branch i Calculate the length coefficient for the ith branch, l i Is the geometric length of the ith branch;
since the tree-like structure usually adopts a circular cross section, the strong axis and the weak axis can be distinguished. According to the formula (1), the stable ultimate bearing capacity of the branch is closely related to the cross-sectional characteristics, the geometric length, the calculated length coefficient and the material properties of the branch. And all branches of the tree structure are added and are instable at the same time, so that the maximization of the integral stable bearing capacity of the tree structure can be ensured. Here, the ratio of the actual internal force of the branch under a given load to the stable bearing capacity is set as R, as shown in (2), when the ratios of the branches are the same, the maximization of the overall stable bearing capacity of the tree-like structure is ensured. Due to branchingThe cross-section is often already determined by design, so E i The calculated length coefficient, which may be considered a constant, is related to the bending stiffness of the node, and may be considered a fixed value for a particular node. Thus, the magnitude of the R value can be varied by the geometric length of the branches.
Step 5.2: calculating the ratio R of the actual internal force to the stable bearing force of the branch under the given load:
wherein R is i Is the ratio of the actual internal force to the steady bearing force of the ith branch under a given load, F i Is the axial internal force of the ith branch;
step 5.3: calculating the average value R of the ratio of the actual internal force to the stable bearing force of the branch under the given load ave ：
Wherein n is the number of all branches; for branches with larger R values, belonging to dangerous branches, the size of R can be reduced by reducing the geometrical length l of the branch. Likewise, for branches with smaller R values, the R value can be increased by increasing the size of l. In the two-element numerical model, the size of the branch geometry can be changed by applying a temperature load. Since the temperature does not exist in reality, it is called a virtual temperature method.
Step 5.4: calculation of R i And R ave Difference Δ R of i When Δ R i When it is negative, i.e. R ave Less than R i Then the internal force of the branch is large, then a negative temperature load is applied to reduce the branch geometry length, otherwise a positive temperature load is applied to increase the branch geometry length:
△R i ＝R ave -R i (4)
step 5.5: calculating the temperature load Δ T of the branch:
wherein, A i Is the cross-sectional area of the ith branch unit, alpha i The linear expansion coefficient of the ith branch;
according to the "barrel theory", the overall stable bearing capacity of the tree structure is determined by the branch with the smallest stable bearing capacity. Therefore, it can be said that when each branch of the tree structure fails simultaneously, the node of the tree structure is located and the branch length is most reasonable. Therefore, the optimization theory research is carried out on the length of each branch according to the Euler stable bearing capacity of the compression bar. The structural hierarchy and branch geometry length of the tree structure are shown in FIG. 6.
And 6: changing the node position according to the extracted node horizontal displacement, wherein the jth node position is changed to: x is a radical of a fluorine atom j ＝x j +d xj ,y j ＝y j +d yj ，x i For the j-th node horizontal x-axis position, y j The y-axis horizontal position of the jth node;
and 7: if m is an even number, applying a temperature load to the tree structure with the double-unit numerical model according to the temperature load numerical value calculated in the step 5;
and 8: in finite element software, the vertical and horizontal freedom degrees of the top node of the tree structure are restrained by applying a displacement restraining mode, and all the freedom degrees of the bottom node of the trunk are restrained simultaneously.
And step 9: and performing nonlinear static analysis, and extracting vertical displacement of all nodes, wherein the vertical displacement of the jth node is as follows: d zj ；
Step 10: changing the node position according to the extraction point vertical displacement, wherein the jth node position is changed to: z is a radical of formula j ＝z j +d zj ，z j Vertical z-axis position for j-th node;
step 11: judging whether the maximum node displacement is less than a threshold value, namely Max (d) xj ,d yj ,d zj )<And (4) error, wherein the error is a threshold, if yes, the shape finding process is ended, otherwise, m is m +1, and the step returns to the step 4 to carry out shape finding again.
To simplify the calculation, the present embodiment sets the calculation length coefficients of all branches at the same stage to the same value. Based on the proposed optimization method, this section performs systematic analysis on the shape finding optimization of the planar tree structure. The section characteristics and the calculated length coefficients of the branches at all levels are set as different parameters, and the section parameters of the trunk and the branches at all levels are shown in table 1. Wherein, I G ，A G And A i ，I i Respectively representing the axial inertia moment and the section area of the trunk and the ith-level branch; the calculated length coefficients for each stage of the branch are shown in table 2. In the same way, mu G And mu i The calculated length coefficients of the trunk and the ith branch are represented, respectively. The loads and initial shape of the tree structure used are shown in figure 7.
TABLE 1 parameters of the section of a planar tree structure in different cases
TABLE 2 calculation of Length coefficients for planar Tree structures under different conditions
Assuming that the section characteristics and the calculated length coefficient of the tree structure respectively adopt S I And mu I And performing shape-finding optimization analysis under the action of given load. Fig. 8 shows the shape of the tree after different iterations. As can be seen from the shown calculation results, unreasonable branch lengths can be optimized quickly by using the proposed method. The cross-sectional area and the axial inertia moment of the trunk are large, and the calculated length coefficient is small, so that the length of the trunk is reduced after iteration. Because the internal force of the edge branch of the tree structure is small, after optimization, the geometric length of the edge branch is generally larger than that of the internal branch of the tree structure. At the same timeIt can also be seen that after 2000 iterations, the shape of the tree structure hardly changes, which indicates that the method is very efficient as a method for finding and optimizing the tree structure.
Fig. 9 is an internal force cloud chart of the optimized tree structure. As can be seen from the figure, the method can also form the tree-shaped structure while optimizing the length of the branch, and the magnitude of the bending moment of the branch after forming is about 1 percent of the axial force and can be basically ignored. The method can couple the optimization work and the shape finding work in an iterative procedure, the convergence speed is high, the node 18 is shown in figure 10, the position is shown in figure 8, and the change process of the displacement in the x direction and the y direction in the convergence process is realized. As can be seen from the figure, the displacement of the node 18 is rapidly reduced to 0, and after about 2500 iterations, the position of the node 18 does not change any more, and the optimized shape finding process of the whole tree structure is completed.
Combining the different parameters shown in table 1 and table 2, respectively, obtains the optimal result of the tree structure under different parameter combinations, as shown in fig. 11. Fig. 11a shows that when the calculated length factor of each branch is the same as the trunk, the trunk length is significantly less than it would otherwise be. As can be seen from FIG. 11c, as the calculated length factor of the branch at level 4 increases, the geometric length of the branch at that level decreases significantly. FIG. 11d also shows that as the calculated length factor for grade 1 branches increases relatively, the geometric length of the grade 1 branches also decreases significantly. Therefore, the calculation results show that the influence of the calculated length coefficient can be accurately reflected in the calculation method.
In practical engineering, the tree structure is spatial. In order to verify the applicability of the method provided by the invention to the spatial tree structure, the section analyzes the optimization form finding of the spatial tree structure, and the established columnar structure is shown in fig. 12. All the vertices of the tree are no longer in one plane but lie in an approximately spherical curve. All nodes exert a concentrated force of 10kN in the vertical direction. The calculated length factor and cross-sectional properties of each branch are shown in tables 3 and 4 for each case.
TABLE 3 calculation of length coefficients for spatial tree structures under different conditions
TABLE 4 Cross-sectional parameters of spatial tree structure under different conditions
The internal force cloud of the optimized tree structure is shown in fig. 13. As can be seen from the calculation results, the axial force of the tree structure is about one twenty-ten-thousandth of the maximum value of the stationery. The bending moment values are so small in relation to the axial forces that they can be neglected, considering the effect of the hand-axial forces of the branches.
The result of the spatial tree structure optimization shaping under different conditions is shown in fig. 14. From the analysis results, the method can quickly and efficiently obtain accurate results in a tree structure in a three-dimensional space, and has strong engineering applicability. Based on S I And mu I The resulting primary branch length is significantly less than that based on S I And mu II The obtained length of the primary branch can be seen from different results, and the calculated length coefficient of the branch can also obtain accurate reaction in the form finding result.
The invention carries out systematic research on the shape-finding optimization of the tree structure. On the basis of the tree structure numerical model established by using double units, a shape finding iterative program of a tree structure is provided, and results show that the iterative program can efficiently and quickly obtain the tree shape meeting the requirements. Under given load, each branch of the tree structure is only acted by axial force, and the bending moment is very small and can be ignored.
On the basis of shape finding, the invention carries out optimization analysis on the branch length of the tree structure based on the compression bar Euler stable bearing capacity. And providing an optimization program based on a virtual temperature method, and combining the shape finding program with the optimization program to provide a strong coupling shape finding optimization algorithm of a tree structure. The method can ensure that each branch of the tree-shaped structure is only acted by an axial force under the action of a given load, and can optimize the length of each branch according to the section characteristic and the internal force of each branch, thereby improving the stable bearing capacity of the whole tree-shaped structure. Analysis results show that the algorithm can be efficiently applied to shape finding analysis of the space tree structure.
The experimental results are as follows:
the result of the tree structure obtained after the shape finding of the invention is compared and researched with the result obtained by Hunt, wherein Hunt is a paper: hunt J, Haase W, Sobek W.A design tool for Spatial tree Structures [ J ] Journal of the International Association for Shell and Spatial Structures,2009,50(1):3-10, as shown in FIG. 5. From the calculation results, the two are highly coincident, which shows that the double-unit-based shape-finding iterative program has high precision and high efficiency, and avoids heavy programming work.
Claims (3)
1. A shape finding optimization design method of a strong coupling tree-shaped structure is characterized by comprising the following processes:
step 1: setting initial parameters according to design requirements, comprising: setting the position of applying load according to design or actual requirements, wherein the node coordinate of applying load is fixed in the iteration process; setting a calculation length coefficient mu of each unit according to the node rigidity;
step 2: establishing a double-unit numerical model, forming a tree structure with the double-unit numerical model according to initial parameters, wherein a trunk is in a vertical direction, each branch of the tree structure is a double-unit numerical model, the double-unit numerical model comprises a beam unit and a rod unit, the section area a of the beam unit and the section area A of the rod unit are set, and the axial inertia moment I of the beam unit is set;
and step 3: setting the initial value of a positive integer m to be 1;
and 4, step 4: if m is an odd number, applying a reverse load, namely a vertically upward point load, to the tree structure with the double-unit numerical model;
and 5: tree structure with double-unit numerical model for applying reverse loadCarrying out nonlinear static analysis to solve the internal force of each branch, wherein the axial internal force of the ith branch is F i (ii) a Extracting all node horizontal displacement, wherein the horizontal displacement of the j-th node is d xj And d yj (ii) a Extracting the geometric length of all branches, wherein the geometric length of the ith branch is l i Calculating the temperature load Delta T of all branches according to the axial force of each branch according to the following steps, including the steps of 5.1-5.5:
step 5.1: obtaining the stable limit bearing capacity F of each branch after optimization according to the compression bar stability and Euler bearing capacity formula cri ：
Wherein, E i Means the modulus of elasticity, I, of the material used for the ith branch i Axial moment of inertia of the beam unit of the i-th branch,/ i Geometric length of the ith branch,. mu. i Means the calculated length coefficient for the ith branch;
step 5.2: calculating the ratio R of the actual internal force to the stable bearing force of the branch under the given load:
wherein R is i Is the ratio of the actual internal force to the steady bearing force of the ith branch under a given load, F i Is the axial internal force of the ith branch;
step 5.3: calculating the average value R of the ratio of the actual internal force to the stable bearing force of the branch under the given load ave ：
Wherein n is the number of all branches;
step 5.4: calculation of R i And R ave Difference Δ R of i When Δ R i When it is negative, i.e. R ave Less than R i Then the internal force of the branch is large, then a negative temperature load is applied to reduce the branch geometry length, otherwise a positive temperature load is applied to increase the branch geometry length:
△R i ＝R ave -R i (4)
step 5.5: calculating the temperature load DeltaT of the branch:
wherein A is i Is the cross-sectional area of the ith branch unit, alpha i The linear expansion coefficient of the ith branch;
step 6: changing the node position according to the extracted node horizontal displacement, wherein the jth node position is changed to: x is the number of j ＝x j +d xj ,y j ＝y j +d yj ，x j For the j-th node horizontal x-axis position, y j The y-axis horizontal position of the jth node;
and 7: if m is an even number, applying a temperature load to the tree structure with the double-unit numerical model according to the temperature load numerical value calculated in the step 5;
and step 8: constraining the vertical and horizontal freedom degrees of the top node of the tree-shaped structure and simultaneously constraining all the freedom degrees of the bottom node of the trunk by applying a displacement constraint mode in finite element software;
and step 9: and performing nonlinear static analysis, and extracting vertical displacement of all nodes, wherein the vertical displacement of the jth node is as follows: d zj ；
Step 10: changing the node position according to the extraction point vertical displacement, wherein the jth node position is changed to: z is a radical of j ＝z j +d zj ，z j Is the vertical z-axis position of the jth node;
step 11: judging whether the maximum node displacement is less than a threshold value, namely Max (d) xj ,d yj ,d zj )<And (4) error, wherein the error is a threshold, if yes, the shape finding process is ended, otherwise, m is m +1, and the step returns to the step 4 to carry out shape finding again.
2. The method of claim 1, wherein the method for establishing a two-unit model comprises: a common beam element numerical model is established in finite element software, a beam element is copied, the copied beam element type is changed into a rod element model, the node number is unchanged, and the beam element and the rod element are called a double-element numerical model together.
3. The shape-finding optimization design method of the strongly coupled tree-like structure according to claim 1, wherein the cross-sectional area of the rod unit in each double-unit numerical model is 100-10000 times that of the beam unit.
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